The Toroidal FCDT is consist of three coils just as the Linear FCDT, but the coils were winded toroidal around a glass tube bent in an O-form. Each secondary coil overlays the half of the torus, and they has around 800-800 turns. The primary coil overlays the the whole torus:

The external radius of the Toroidal FCDT is R = 80 mm, the internal radius is r = 3 mm. The inner cell is precisely half-filled with ferrofluid, thus the volume of the fluid in the cell is And the volume of ferrofluid is divided amongst the two secondary coils depending on the tilt of the sensor. It is obvious that when rotating the sensor, the amount of ferrofluid in the secondary coils is changing linearly with the tilt. In cases of α = 0 ° and α = 180 ° there is an equal volume of ferrofluid in the secondary coils. In cases of α = 90 ° and α = 270 ° the ferrofluid is always in just one secondary coil. It can be seen on the diagram below:

Next post: Experimental and theoretical curves of the Toroid FCDT (https://hackaday.io/project/11225-a-new-high-accuracy-tilt-sensor/log/46956-experimental-and-theoretical-curves-of-the-toroid-fcdt)